On singularities of value function for Bolza optimal control problem ✩

We study the set of points of nondifferentiability, called the singular set, of the value function of a Bolza optimal control problem. The value function is a viscosity solution to an associated Hamilton– Jacobi equation. The method of characteristics associates to this equation a Hamiltonian system, that in turn can be used to study the propagation of singularities of the value function. In particular, we obtain an extension of the Rankine–Hugoniot type condition, which is well-known in the conservation law theory.  2004 Elsevier Inc. All rights reserved